Is the word livre the same in Brazilian and European Portuguese?

Yes

The meaning, spelling, and grammatical function of "livre" are identical in both Brazilian and European Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the final "e" is typically vocalized as a reduced "i" sound (sounding like leev-ree). In European Portuguese, the final "e" is much more closed and often nearly silent, making the word sound closer to leevr.

Brazilian Portuguese Examples

1. Você está livre amanhã? (Are you free tomorrow?)
2. Eu me sinto livre para dizer a verdade. (I feel free to tell the truth.)
3. O trânsito está livre na rodovia. (Traffic is clear on the highway.)
4. Ela quer ser uma mulher livre. (She wants to be a free woman.)
5. O campo está livre de animais. (The field is free of animals.)

European Portuguese Examples

1. Estás livre amanhã? (Are you free tomorrow?)
2. Sinto-me livre para dizer a verdade. (I feel free to tell the truth.)
3. O trânsito está livre na autoestrada. (Traffic is clear on the highway.)
4. Ela quer ser uma mulher livre. (She wants to be a free woman.)
5. O campo está livre de animais. (The field is free of animals.)